Question

Let $h(x)=f(g(x)),$ where $f$ and $g$ are differentiable on their domains. If $g(1)=3$ and $g^{\prime}(1)=5,$ what else do you need to know to calculate $h^{\prime}(1) ?$

   Let $h(x)=f(g(x)),$ where $f$ and $g$ are differentiable on their domains. If $g(1)=3$ and $g^{\prime}(1)=5,$ what else do you need to know to calculate $h^{\prime}(1) ?$

Calculus for Scientists and Engineers: Early Transcendental

William Briggs, Lyle… 1st Edition

Chapter 3, Problem 2

Instant Answer

Solved by Expert Amy Jiang

05/27/2020

Step 1

The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function, times the derivative of the inner function. In mathematical terms, this gives us $h'(x) = f'(g(x)) \cdot g'(x)$. Show more…

Show all steps

Thanks for your feedback!

Let $h(x)=f(g(x)),$ where $f$ and $g$ are differentiable on their domains. If $g(1)=3$ and $g^{\prime}(1)=5,$ what else do you need to know to calculate $h^{\prime}(1) ?$

Play audio

Feedback

Amy Jiang and 98 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Composite Functions

Composite functions involve combining two functions such that the output of one function becomes the input of another. This concept is fundamental in calculus when analyzing how changes in one variable affect another through an intermediary function.

Chain Rule

The chain rule is a formula used to compute the derivative of composite functions. It states that the derivative of h(x) = f(g(x)) is h'(x) = f'(g(x)) · g'(x). To apply the chain rule at a specific point, you need to know both the derivative of the outer function evaluated at the inner function’s value and the derivative of the inner function at that point.

Please give Ace some feedback